Use a graphing calculator to graph each equation in the standard viewing window. 3x + 4y = 6

Verified step by step guidance

1. Rewrite the given equation \(3x + 4y = 6\) in slope-intercept form \(y = mx + b\) by isolating \(y\). Start by subtracting \(3x\) from both sides: \(4y = -3x + 6\).
2. Next, divide every term by 4 to solve for \(y\): \(y = \frac{-3}{4}x + \frac{6}{4}\). Simplify the fraction \(\frac{6}{4}\) if possible.
3. Turn on your graphing calculator and enter the function \(y = -\frac{3}{4}x + \frac{3}{2}\) into the function input (usually labeled as \(Y=\)).
4. Set the graphing window to the standard viewing window, which typically has \(x\) and \(y\) values ranging from -10 to 10. This ensures you see the main features of the graph.
5. Graph the equation and observe the line. Note the slope \(-\frac{3}{4}\) which indicates the line falls 3 units vertically for every 4 units it moves horizontally, and the y-intercept \(\frac{3}{2}\) where the line crosses the y-axis.

Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are constants. Understanding this form helps in identifying the coefficients and constants needed to graph the line or convert it into slope-intercept form for easier plotting.

Graphing Linear Equations Using a Calculator

Graphing calculators allow you to input equations and visualize their graphs quickly. For linear equations, you often need to solve for y or use the calculator’s function input to plot the line within the standard viewing window, typically set from -10 to 10 on both axes.

Standard Viewing Window

The standard viewing window on a graphing calculator usually ranges from -10 to 10 on both the x- and y-axes. Knowing this helps you anticipate how the graph will appear and ensures the important features of the line, such as intercepts, are visible within this range.